Lawrence is aiming to maintain his place in the England Test side after a successful debut winter and gave the selectors a jolt with his first century of the season - the fastest and the 11th in his first-class career.
Tom Westley also smashed 106, in a 221-run stand with Lawrence, while Nick Browne and Sir Alastair Cook also picked up half-centuries.
Essex eventually declared on 413 for three, after Lawrence had dispatched Matt Critchley for three consecutive sixes, before Derbyshire slumped to close on 35 for three.
No play was possible on the first day but Derbyshire won the toss – something they might have regretted as Essex scored at will.
Billy Stanlake endured a torrid first spell for his county as he struggled with his run-up – bowling six no balls in four overs, while also pulling out of a similar number of deliveries as he approached the crease.
Browne scored his fifty in 92 balls and Cook in 72. It was the sixth time Browne had past fifty in seven innings against Derbyshire – with an average of 213.25 against the county.
After a season-high opening stand of 137, both openers fell in four balls of each other to Stanlake, who found more stability at the River End.
Browne was tempted to drive at a full and wide delivery only for Stanlake’s express pace to see him edge to first slip, while Cook wobbled a chip up to extra cover.
That brought Lawrence and Westley to the wicket. Half-centuries were brought up in a sensible 66 and 75 deliveries before the game plan switched to outright attack.
Lawrence moved to his first hundred since 2016 in 112 balls needing a further 20 deliveries to pass 150.
Lawrence played some outrageous shots in his innings but none more so than the guided pull six off Stanlake before dispatching Critchley into the river, two of six maximums alongside 16 fours.
Westley, who eventually holed out to deep extra cover for 106, was no less expansive with 15 boundaries and a six – he rapidly expanded from fifty to a ton in 34 balls.
Skipper Westley called in quits with maximum batting points secured, after Lawrence and Walter had thrashed 53 runs in four overs – Essex scoring 234 of their runs in boundaries.
The scorecard did not make pretty reading for the bowlers, with Luis Reece the only to record an economy of under four an over.
Bad light meant Essex could only bowl spinners Simon Harmer and Dan Lawrence but Reece was lbw to the former, Billy Godleman was caught at short leg and Leus du Plooy pushed to second slip.